The meaning of the word is undisputed.
Interestingly — the Yiddish spelling (above) ends with an “ayin,” which usually represents the phoneme “eh” or the Hebrew vowel “seghol,” which has the same sound. It suggests that the correct pronunciation is actually “Lat-keh,” with an “eh” ending rather than a short “a.”
“Lat-kee,” as is occasionally heard, can be tolerated as a well-meaning try. The error is understandable, given the standard English spelling. Perhaps we should insist on “latkeh?”
There’s some question about where the word itself comes from:
“…from…Russian латка (látka, ‘pastry, patch’).” 
[Note that in the above example, the author spelled the Russian word with a “T,” whereas examples given below spell it with a “D” (based on the Greek “delta”). The use of the “D” would correspond more closely to the Greek original. “T” is the unvoiced form of “D.” As it’s spelled with a “T” (“Tet”) in Hebrew/Yiddish, I’m guessing that accurately conveys the Russian spelling and pronunciation that Jewish culture received.
He also spelled it in Russian without the initial “O” found in the examples below.]
This derivation, however, is elsewhere refuted:
“…the [Oxford English Dictionary] does say it’s from Russian, ‘latka’ meaning ‘pastry,’ but …none of the Russian dictionaries I have consulted have that definition. ‘Latka’ can mean an ‘earthenware vessel,’ as the Shorter Oxford says, but in that sense it is a dialect word used in St Petersburg and the North. I got that from an online etymological dictionary. The Russian dictionaries I have at home…give just one definition of ‘latka’ and that is ‘patch’ — i.e. a piece of material sewn on ragged clothing. So that could be it, with the latkes either being the shape of a patch or so-called because of the ‘poor man’ connection as mentioned by Phyllis Glazer. I have eaten olad’i in Russia; they are small thick pancakes with yeast being an obligatory ingredient.” 
The mention of “olad’i” leads to another derivation:
“…the Yiddish לאטקע (latke) came from the Ukrainian оладка (oladka), which several online dictionaries faithfully translate as ‘pancake,’ ‘fritter,’ ‘flapjack,’ and the like (‘muffin’ seems to be in there too for some reason). This is a diminutive of the Old Russian оладья (olad’ya) [‘ke’ or ‘ka’ is the diminutive ending, used to denote affection or small size].”
Now it gets interesting: this comes from the Greek ελαδια (eladia), plural of ελαδιον (eladion), meaning ‘a little oily thing,’ ‘a little oil,’ or ‘a young olive tree.’ Which proudly paves the way to eladion being a diminutive of elaion, ‘olive oil,’ which in turn comes from elaia, the (Ancient) Greek for ‘olive.’
So, centuries later, five languages away, and twice miniaturised, we get our ‘little tiny things made of (olive) oil’ – latkes.” 
Matthew Goodman (see below) notes that it could also be associated with the Belarussian аладка (aladka) — which has the same meaning as the Russian and Ukrainian words (note the initial short “A” rather than the short “O,” to capture the short “E” in the Greek, although there’s probably not much difference in the actual pronunciation).
This is slightly more understandable if the initial vowel in the Russian, Belarussian and Ukrainian is pronunced as a short “O,” as in “other.” The transition from the Greek to the later three would then be all the more noticeable. By the time it gets to Yiddish, the initial vowel is dropped completely — to save time?
Also — in the Greek and the old Russian, the middle consonant is d/delta. In later Russian, it becomes “T,” which then appears in Yiddish as “Tet.” “T” is the unvoiced form of the same phoneme of which “D” is the voiced form. So, in some alternate universe, we might be eating “ladkes” — even “lad’kehs” — on Hanukah.
How the word got from Greek to Russian isn’t entirely clear. Howard Goldman provided an explanation in a comment to my link on Facebook to this post. [see below *]
So, “latke,” eaten on a holiday that commemorates the Jewish victory over the Seleucid Greeks, comes from a Greek word that came into Russian, etc., by way of the Greek Orthodox Church [*]? Ergo, if not for the Greeks and the Church, we wouldn’t have “latke?” We should hardly overlook the irony of that! There’s a great drash in there, somewhere.
Russian, Ukrainian and Greek are all Indo-European languages. An ancient branch of the same family is Sanskrit. In Sanskrit, “oil” is “taila.” Some linguist could probably argue that there’s a connection between “taila” and “”eladia” by inverting the “L” and the “T” and substituting a “D” for the “T.” They do that so often, don’t they? But of course, Sanskrit ceased to be a spoken language long before “latkes” were around.
Finally, from a comprehensive Forward article:
The Story of the Ever-Evolving Latke:
On Chanukah, Cheese Was the Norm, But Then Came the Potato
The Food Maven (column)
by Matthew Goodman
“According to the Oxford English Dictionary, which knows about this sort of thing, the first published reference to latkes in the United States dates to 1927, specifically to the phrase ‘luscious potato latkes — pancakes made of grated, raw potatoes,’ from an article in H.L. Mencken’s monthly, The American Mercury. The OED goes on to note several subsequent citations, mostly from cookbooks, but among them an aside from the great 1964 comic novel, ‘To an Early Grave‘: ‘I make a few latkes, I paint the kitchen chairs.’ Though surely of limited etymological use, the citation is delightful nonetheless, if only for the notion of the Oxford English Dictionary quoting Wallace Markfield.
In any case, by the third decade of the 20th century, when The American Mercury first announced them to the general public, latkes were already commonplace in Yiddish literature — as in, for example, Sholom Aleichem’s 1900 story ‘Khanike Gelt’ (Chanukah Money), which begins: ‘Can you guess, children, which is the best of all holidays? Chanukah, of course. You don’t go to school for eight days in a row, you eat latkes every day…’ The reason for the time lag, needless to say, is that ‘latke’ is Yiddish and, like most immigrant parlance, took a while to find its way into the pages of English. The Yiddish word is thought likely to derive from the Russian [or Ukrainian] ‘oladka,’ the diminutive of ‘oladya,’ defined as ‘a flat cake of unleavened wheat dough.” (Alternatively, it may come from the Belarussian ‘aladka,’ a word with a similar meaning.) The etymological sources agree that the word seems to have descended from the Middle Greek ‘eladion,’ an oil cake (the American Heritage Dictionary prefers to define it as a ‘little oily thing’), derived from the Greek ‘elaion,’ meaning ‘olive oil.’
The distance from the Yiddish ‘latke’ to the Greek ‘elaion’ is about as vast as the Diaspora itself, but the relationship is interesting because the first latkes were little cakes made from curd cheese and fried in butter or olive oil. (Eating cheese on Chanukah is said to refer to the Apocryphal story of Judith, who fed salty cheesecakes to the Syrian general Holofornes to make him thirsty, and then plied him with wine until he was so inebriated she could chop off his head with a sword; this symbolic connection, though, was not made until many centuries after the first cheese latkes.[**]) As Jews began to migrate eastward into Eastern Europe, butter and oil grew increasingly precious and expensive, and poultry fat became the chief frying agent; this made the use of cheese off-limits, and so by the Middle Ages latkes were most often made not from dairy ingredients but rather with a simple batter made from buckwheat flour (recall the original Russian meaning of ‘a flat cake made from unleavened wheat flour’).
As for the potato, it was certainly not finding its way into any latkes at that time, because potatoes were unknown in Europe until the late 16th century, when they were shipped back from the New World by Spanish conquistadors. Further complicating matters, potatoes were rumored to be a carrier of typhoid and leprosy and were not widely planted in Europe until disastrous harvests of the staple grains left farmers no alternatives. This happened in stages throughout the continent, beginning in Germany in 1720 and culminating in Russia by the 1840s; it is only at this time, the mid-19th century, that we first start to see references to latkes being made from potatoes. Sometimes the latkes were made with potato flour, after the earlier buckwheat version, but more often they were made in a new way, by grating the potatoes and frying them in rendered chicken fat or, more luxuriously, goose fat. Geese, which were fattened in summer and fall and slaughtered when the weather turned cold, were especially plentiful just before Chanukah, and so it is no surprise that latkes fried in goose fat would become a trademark of this holiday celebrating fried foods; often the latkes were served with the roasted goose, which would be a worthy feast for almost anyone, but for impoverished shtetl peasants it must have seemed a glimpse of paradise.
Even without a crackling roast goose alongside them, potato latkes are about the most satisfying food imaginable — hot, crispily browned, slightly salty, shimmering with a patina of oil. Though their pedigree is shorter than we might have suspected, by now potato latkes have become the very embodiment of Jewish-American holiday food, and the subject of impassioned debate about the best way to make them. The intensity of these arguments recalls those about the making of matzo balls, the other Jewish-American holiday food nonpareil, but while I tend to be a middle-of-the-roader on the matzo-ball question, when it comes to potato latkes I am a Maccabee-like partisan.
The latke must be thin rather than thick (if the fryable surface area is too small, the latke will never attain the necessary crispness) and must be made from starchy Russet potatoes (not the waxy red-skinned variety; and though Yukon Gold are said to work, the idea of it seems to me a bit precious). If at all possible, the potatoes should be hand grated; only hand grating can create the chunky texture that defines the genuine potato latke.
Still, as we have seen, latkes were made for a long time without potatoes, and now they are being so once again, thanks to a new wave of latkes made by modern chefs. In these latkes, the potatoes have been replaced — or sometimes supplemented — with sweet potatoes, carrots, parsnips, turnips, celery root, cauliflower and almost every other form of gratable vegetable. To my mind there is no improving on perfection, but even I don’t want to eat potato latkes (as Sholom Aleichem’s schoolchildren did) for eight straight days, so I’m happy for a good alternative — such as, for instance, beet latkes. These pancakes, vegetally sweet, are made just as one would the potato variety (though you should use more flour, as beets are less starchy than potatoes, and it’s also nice to add some grated orange zest). In this case, I recommend replacing the traditional sour cream topping with goat cheese, because its salty creaminess goes astonishingly well with beets, and never more so than when the beets are piping hot from the frying pan, causing the goat cheese to melt lusciously into them. It is, as Wallace Markfield might say, a mechaiah.”
 http://nancyfriedman.typepad.com/away_with_words/2008/12/word-of-the-week-latke.html (in a reply to the author’s article)
[*] “The word migrated from Greek to Russian through a well-trod path.
There was a major trade route from Greece through Bulgaria to medieval ‘Rus,’ which was the mother of the future Russia, which at that time was centered around Kiev, Ukraine.
This path was trod also by Greek Orthodox priests, who brought their religion east to Bulgaria, where it became medieval Bulgarian Orthodoxy, and north to Kiev, where it developed into Russian Orthodoxy. Not just religion flowed north to Rus, but words and things, including oil, fried foods, and the Slavic alphabet, based mostly on Greek, and partly on Hebrew.”
[**] I would also point out that the book of “Yehudit/Judith,” while originally written in Hebrew and appearing in Greek in the Septuagint, is barely known among Jews. I doubt there’s any connection between the book, the holiday, and the latke.